1. Field of the Invention
The present invention relates to a specification determining method, a projection optical system making method and adjusting method, an exposure apparatus and making method thereof, and a computer system, and more specifically to a specification determining method of determining the specification of a projection optical system to be provided in an optical apparatus, a method of making and a method of adjusting a projection optical system to be provided in an optical apparatus, an exposure apparatus provided with the projection optical system made according to the method of a projection optical system and making method thereof, and a computer system suitable for implementing the specification determining method and adjusting the imaging characteristic of the projection optical system provided in the exposure apparatus.
2. Description of the Related Art
In a lithography process for manufacturing semiconductor devices (CPU, DRAM, etc.), image picking-up devices (CCD, etc.), liquid crystal display devices, membrane magnetic heads or the like, exposure apparatuses have been used which form device patterns on a substrate. Because of increasingly high integration of semiconductor devices in these years, a step-and-repeat type of reduction projection exposure apparatus (the so-called stepper) that can form fine patterns on a substrate such as a wafer or glass plate, a step-and-scan type of scan projection exposure apparatus (the so-called scanning stepper) that is improved over the stepper, or the like is mainly used.
In the process of manufacturing semiconductor devices, because multiple layers each of which has a sub-circuit pattern need to be overlaid and formed on a substrate, it is important to accurately align a reticle (or mask) having a sub-circuit pattern formed thereon with respect to the already-formed pattern in each shot area on a substrate. In order to accurately align, the optical characteristic of the projection optical system needs to be precisely measured and adjusted to be in a desired state (for example, a state where magnification error of the transferred image of a reticle pattern relative to each shot area's pattern on the substrate is corrected). It is remarked that, also when transferring a reticle pattern for a first layer onto each shot area of the substrate, the imaging characteristic of the projection optical system is preferably adjusted in order to accurately transfer reticle patterns for second and later layers onto each shot area.
As the method of measuring the optical characteristic (the imaging characteristic, etc.) of the projection optical system, a method is mainly used which calculates the optical characteristic based on the result of measuring a resist image obtained by exposing a substrate through a measurement reticle having a predetermined measurement pattern that remarkably responds to a specific aberration, formed thereon and then developing the substrate where the projected image of the measurement pattern is formed, the method being called a “print method”, hereinafter.
In exposure apparatuses of the prior art, measuring lower-order aberrations such as Seidel's five aberrations, i.e., spherical aberration, coma, astigmatism, field curvature, and distortion according to the print method and adjusting and managing the above aberrations due to the projection optical system based on the measuring result has been performed.
For example when measuring distortion due to the projection optical system, a measurement reticle is used on which inner box marks that each are a square having a dimension of 100 um and outer box marks that each are a square having a dimension of 200 um are formed, and after having transferred the inner or outer box marks onto a wafer whose surface is coated with a resist through the projection optical system, the wafer stage is moved and then the other marks are transferred and overlaid onto the wafer through the projection optical system. When the magnification is equal to ⅕ for example, the resist image of box-in-box marks appears, after development of the wafer, in each of which a box mark having a dimension of 20 um is located inside of a box mark having a dimension of 40 um. And distortion due to the projection optical system is detected by measuring the positional relation between both the marks and deviation from their reference point in the stage coordinate system.
Moreover, when measuring the coma, a measurement reticle is used on which a line-and space pattern (hereinafter, referred to as a “L/S”) having five lines whose width is, for example, 0.9 um is formed, and the pattern is transferred onto a wafer whose surface is coated with a resist through the projection optical system. When the magnification is equal to ⅕ for example, the resist image of the L/S pattern appears, after development of the wafer, having a line width of 0.18 um. And coma due to the projection optical system is detected by measuring the widths L1, L5 of two lines in both ends of the pattern and obtaining a line-width abnormal value given by the following equation:the line-width abnormal vale=(L1−L5)/(L1+L5)  (1).
Moreover, in measuring a best focus position of the projection optical system, a wafer is moved sequentially to a plurality of positions along the optical axis direction which are a given distance (step pitch) apart from each other, and the L/S pattern is transferred each time onto a different area of the wafer through the projection optical system. The wafer position associated with one whose line width is maximal out of the resist images of the L/S pattern, which appear after development of the wafer, is adopted as the best focus position.
When measuring the spherical aberration, the measurement of a best focus position is performed a plurality of times each time with a different L/S pattern having a different duty ratio, and based on the differences between the best focus positions, the spherical aberration is obtained.
When measuring the field curvature, the measurement of a best focus position is performed in a plurality of measurement points within the field of the projection optical system, and based on the measuring results, the field curvature is calculated using the least-squares method.
In addition, when measuring the astigmatism due to the projection optical system, the measurement of a best focus position is performed with two kinds of periodic patterns whose period directions are perpendicular to each other, and based on the difference between the best focus positions, the astigmatism is calculated.
In the prior art, the specification of a projection optical system in the making of an exposure apparatus is determined according to the same standard as in the above managing of the optical characteristic of the projection optical system. That is, the specification is determined such that the five aberrations measured by the print method or obtained by a simulation substantially equivalent thereto are at or below given respective values.
However, because of the demand for further improved exposure accuracy corresponding to increasingly high integration in these years, measuring only the lower-order aberrations according to the prior art method and, based on the measuring result, adjusting the optical characteristic of the projection optical system does not yield a desired result. The reason for that is as follows.
The space image of a measurement pattern, for example, a L/S pattern has space-frequency components (intrinsic frequency components), i.e. a fundamental wave corresponding to the L/S period and higher harmonics, and the pattern determines the space-frequencies of the components that pass through the pupil plane of the projection optical system. Meanwhile, reticles having various patterns are used in the actual manufacturing of devices, the space images of which patterns include innumerable space-frequency components. Therefore, the prior art method of measuring and adjusting aberrations based on the limited information hardly meet the demand for further improved exposure accuracy.
In this case, although reticle patterns having intrinsic frequency components that are missing in the information need to be measured, it takes an enormous amount of measurement and time, so that it is not practical.
Furthermore, because of the accuracy in measuring resist images, which are affected by the intrinsic characteristic of the resist, etc., the correlation between the resist image and a corresponding optical image needs to be found before extracting data from the measuring result.
Furthermore, when an aberration is large, the linearity of the resist image to the corresponding space image of the pattern is lost, so that accurate measurement of the aberration is difficult. In this case, for the purpose of accurately measuring the aberration, it is necessary to change the pattern-pitch, the line width (space frequency), etc., of the measurement pattern of the reticle, through trial and error, such that the intrinsic characteristic of the resist can be measured (the linearity is obtained).
For the same reason, the method of determining the specification of a projection optical system according to the above criteria has reached its limit. It is because a projection optical system satisfying the specification determined obviously cannot achieve exposure accuracy demanded at present and in the future.
In such circumstances, the adjusting method has been adopted where, when making a projection optical system according to the specification determined, the positions, etc., of lens devices are adjusted such that the Seidel's five aberrations (lower-order aberrations) satisfy the determined specification, based on the result of measuring the aberration due to the projection optical system according to the print method after the assembly of the projection optical system in the making process, and, after that, detecting residual higher-order aberrations by a light-rays tracing method and adjusting the positions, etc., of lens devices in the projection optical system (additionally reprocessing such as non-spherical-surface process, if necessary) are performed (refer to Japanese Patent Laid-Open No. 10-154657).
However, the above method of making a projection optical system needs the two steps of correcting lower-order aberrations and correcting higher-order aberrations and also computation for light-rays tracing that even super-computer will take several days to perform.
Furthermore, when an aberration (non-linear aberration) occurs by which the linearity of the resist image to the corresponding space image of a pattern is lost, adjusting the projection optical system in view of the order in which aberrations are adjusted is needed. For example, when coma is large, the image of a pattern is not resolved, so that accurate data of distortion, astigmatism and spherical aberration cannot be obtained. Therefore, it is necessary to measure coma using a pattern for accurate measurement of coma and adjust the projection optical system to make the coma small enough and then measure distortion, astigmatism and spherical aberration and, based on the measuring result, adjust the projection optical system. The fact that the order of measuring the aberrations to be adjusted is specified means that the selection of the lenses used is restricted.
In addition, the prior art method uses, regardless of what maker the user of the exposure apparatus is, measurement patterns suitable to measure the respective aberrations by in order to determine the specification of the projection optical system and adjust the optical characteristic, the measurement patterns remarkably responding to the respective aberrations.
Meanwhile, the effects that the aberrations due to the projection optical system have on the imaging characteristic for various patterns are different. For example, contact-hole features are more influenced by astigmatism than by the others while a fine line-and-space pattern is more influenced by coma than by the others. Furthermore, the best focus position is different between an isolated line and line-and-space pattern.
Therefore, the optical characteristic (aberrations, etc.) of the projection optical system and other capabilities of an exposure apparatus actually differ between its users.